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On the Limit Behavior of a Chi-Square Type Test if the Number of Conditional Moments Tested Approaches Infinity

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  • de Jong, R.M.
  • Bierens, H.J.

Abstract

In this paper, a consistent model specification test is proposed. Some consistent model specification tests have been discussed in econometrics literature. Those tests are consistent by randomization, display a discontinuity in sample size, or have an asymptotic distribution that depends on the data-generating process and on the model, whereas our test does not have one of those disadvantages. Our test can be viewed upon as a conditional moment test as proposed by Newey but instead of a fixed number of conditional moments, an asymptotically infinite number of moment conditions is employed. The use of an asymptotically infinite number of conditional moments will make it possible to obtain a consistent test. Computation of the test statistic is particularly simple, since in finite samples our statistic is equivalent to a chi-square conditional moment test of a finite number of conditional moments.

Suggested Citation

  • de Jong, R.M. & Bierens, H.J., 1994. "On the Limit Behavior of a Chi-Square Type Test if the Number of Conditional Moments Tested Approaches Infinity," Econometric Theory, Cambridge University Press, vol. 10(01), pages 70-90, March.
  • Handle: RePEc:cup:etheor:v:10:y:1994:i:01:p:70-90_00
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    Cited by:

    1. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens & Oscar A. Mitnik, 2008. "Nonparametric Tests for Treatment Effect Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 389-405, August.
    2. Kasparis, Ioannis & Andreou, Elena & Phillips, Peter C.B., 2015. "Nonparametric predictive regression," Journal of Econometrics, Elsevier, vol. 185(2), pages 468-494.
    3. Koenker, Roger & Machado, Jose A. F., 1999. "GMM inference when the number of moment conditions is large," Journal of Econometrics, Elsevier, vol. 93(2), pages 327-344, December.
    4. Anatolyev, Stanislav, 2012. "Inference in regression models with many regressors," Journal of Econometrics, Elsevier, vol. 170(2), pages 368-382.
    5. repec:taf:jnlasa:v:112:y:2017:i:519:p:1064-1075 is not listed on IDEAS
    6. Delgado, Miguel A. & Domínguez, Manuel A., 1997. "Consistent specification testing of quantile regression models," DES - Working Papers. Statistics and Econometrics. WS 6211, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2003. "Empirical likelihood estimation and consistent tests with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 117(1), pages 55-93, November.
    8. Tue Gørgens & Allan Würtz, 2012. "Testing a parametric function against a non‐parametric alternative in IV and GMM settings," Econometrics Journal, Royal Economic Society, vol. 15(3), pages 462-489, October.
    9. Otsu, Taisuke & Xu, Ke-Li & Matsushita, Yukitoshi, 2015. "Empirical likelihood for regression discontinuity design," Journal of Econometrics, Elsevier, vol. 186(1), pages 94-112.
    10. Karun Adusumilli & Taisuke Otsu, 2017. "Empirical Likelihood for Random Sets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1064-1075, July.
    11. Ignacio N. Lobato, 2000. "A Consistent Test for the Martingale Difference Assumption," Econometric Society World Congress 2000 Contributed Papers 0278, Econometric Society.
    12. Hill Jonathan B., 2013. "Stochastically weighted average conditional moment tests of functional form," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(2), pages 121-139, April.
    13. Demian Pouzo, 2014. "Bootstrap Consistency for Quadratic Forms of Sample Averages with Increasing Dimension," Papers 1411.2701, arXiv.org, revised Aug 2015.
    14. repec:eee:econom:v:200:y:2017:i:1:p:1-16 is not listed on IDEAS
    15. Gupta, A, 2015. "Nonparametric specification testing via the trinity of tests," Economics Discussion Papers 15619, University of Essex, Department of Economics.
    16. Ait-Sahalia, Yacine & Bickel, Peter J. & Stoker, Thomas M., 2001. "Goodness-of-fit tests for kernel regression with an application to option implied volatilities," Journal of Econometrics, Elsevier, vol. 105(2), pages 363-412, December.
    17. repec:cep:stiecm:/2014/574 is not listed on IDEAS
    18. repec:esx:essedp:774 is not listed on IDEAS
    19. Paulo Parente & Richard Smith, 2012. "Exogeneity in semiparametric moment condition models," CeMMAP working papers CWP30/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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